Ngā Tauira Pātai me te Kōrero mō te Tātari Hononga
Ko te tātari hononga he tikanga tatauranga e whakamahia ana hei whakatau i te nui o te whanaungatanga i waenga i ngā taurangi e rua. He maha ngā whakamahinga o tēnei tātari i roto i ngā momo marautanga, tae atu ki te ōhanga, te hinengaro, te rongoā, me te pāpori, hei mārama ki te tata o te whanaungatanga o ngā taurangi e rua. I roto i tēnei tuhinga, ka matapakihia e mātou ētahi tauira raruraru me ngā kōrero hei āwhina i te mārama ki te ariā o te tātari hononga.
Te Mārama ki te Tātari Hononga
Ka whakamahia te tātari hononga hei ine i te kaha me te ahunga o te whanaungatanga i waenga i ngā taurangi tau e rua. Ko te tikanga ka whakaatuhia tēnei uara hononga mā te whakamahi i tētahi tauwehenga hononga, ka taea te awhe mai i te -1 ki te 1. Ka taea te whakamārama i ēnei uara penei:
– +1 : He hononga pai tino pai. Ka neke ngā taurangi e rua i te ahunga kotahi.
– 0 : Kāore he hononga. Kāore he hononga rārangi mārama o ngā taurangi e rua.
– -1 : He hononga kino tino tika. Ka neke ngā taurangi e rua i ngā ahunga rerekē.
Ko te tauwehenga taunga e whakamahia whānuitia ana ko te tauwehenga Pearson. Heoi anō, kei reira anō ētahi atu tikanga tauwehenga, pērā i a Spearman rāua ko Kendall, e pai ake ana mō ngā raraunga raupapa, raraunga kore-raina rānei.
Ngā Hipanga Tātari Hononga
1. Kohikohi Raraunga: Kohikohia ngā raraunga mō ngā taurangi e rua hei tātaritanga.
2. Whakaaturanga Raraunga: Waihangahia he kauwhata marara hei tiro i te tauira whanaungatanga i waenga i ngā taurangi e rua.
3. Tātaitanga o te Tauwehenga Hononga: Tātaihia te tauwehenga hononga Pearson, Spearman, Kendall rānei.
4. Te Whakamārama i ngā Hua: Whakatauhia te kaha me te ahunga o te whanaungatanga i runga i te uara tauwehenga hononga.
5. Whakamātautau Hiranga: Whakatauhia mēnā he hiranga ā-tatauranga te hononga i kitea.
Ngā Pātai Tauira me te Kōrero
Pātai 1: Te Hononga Pearson
Ko ngā raraunga mō te teitei (cm) me te taumaha (kg) o te 5 tāngata e whai ake nei:
| Tangata | Teitei (cm) | Taumaha (kg) |
|——-|—————-|—————|
| A | 160 | 55 |
| B | 165 | 60 |
| C | 170 | 65 |
| D | 175 | 70 |
| E | 180 | 75 |
Tātaihia te tauwehenga taunga Pearson mō ngā raraunga.
Kōrero:
1. Te Tātai i te Toharite:
– Teitei toharite (X̄) = (160 + 165 + 170 + 175 + 180) / 5 = 170
– Taumaha toharite (Ȳ) = (55 + 60 + 65 + 70 + 75) / 5 = 65
2. Te Tātai i te Rerekētanga mai i te Toharite:
– Te rerekētanga teitei: (160 – 170), (165 – 170), (170 – 170), (175 – 170), (180 – 170)
– He rerekētanga nui: (55 – 65), (60 – 65), (65 – 65), (70 – 65), (75 – 65)
3. Te Tatau i te Hua Whakarerekētanga:
– (160-170)(55-65) = 10 10 = 100
– (165-170)(60-65) = 5 5 = 25
– (170-170)(65-65) = 0 0 = 0
– (175-170)(70-65) = 5 5 = 25
– (180-170)(75-65) = 10 10 = 100
Tapeke = 100 + 25 + 0 + 25 + 100 = 250
4. Te Tatau i te Tapawhā o te Ine:
– Teitei: (160-170)², (165-170)², (170-170)², (175-170)², (180-170)²
– Taumaha: (55-65)², (60-65)², (65-65)², (70-65)², (75-65)²
Mō te teitei:
– (160-170)² = 100
– (165-170)² = 25
– (170-170)² = 0
– (175-170)² = 25
– (180-170)² = 100
Tapeke = 100 + 25 + 0 + 25 + 100 = 250
Mō te taumaha:
– (55-65)² = 100
– (60-65)² = 25
– (65-65)² = 0
– (70-65)² = 25
– (75-65)² = 100
Tapeke = 100 + 25 + 0 + 25 + 100 = 250
5. Te Tātai i te Tauwehenga Taurite Pearson:
\[
r = \frac{\tapeke ((X – X̄)(Y – Ȳ))}{\sqrt{\tapeke (X – X̄)² \tapeke (Y – Ȳ)²}}
\]
\[
r = \frac{250}{\sqrt{250 \times 250}} = \frac{250}{250} = 1
\]
Whakamārama: Ko te uara tauwehenga taurite Pearson o te 1 e tohu ana i tētahi whanaungatanga tino pai i waenga i te teitei me te taumaha.
Pātai 2: Te Hononga Spearman
E whai ake nei ngā raraunga whakatauranga o ngā taurangi e rua:
| Tangata | Taurangi X | Taurangi Y |
|——-|—————|————|
| A | 1 | 3 |
| B | 2 | 1 |
| C | 3 | 4 |
| D | 4 | 2 |
| E | 5 | 5 |
Tātaihia te tauwehenga taunga Spearman i runga i ngā raraunga.
Kōrero:
1. Te Tātaitanga o te Rerekētanga Whakatauranga (d):
– Mō te Whakatauranga X me Y:
– A: 1 – 3 = -2
– B: 2 – 1 = 1
– C: 3 – 4 = -1
– D: 4 – 2 = 2
– E: 5 – 5 = 0
2. Te Tātaitanga o te Tapawhā o te Rerekētanga o te Whakatauranga (d²):
– (-2)² = 4
– (1)² = 1
– (-1)² = 1
– (2)² = 4
– (0)² = 0
Tapeke (Σd²) = 4 + 1 + 1 + 4 + 0 = 10
3. Te tatau i te tauwehenga hononga Spearman:
\[
r_s = 1 – \frac{6 \sum d^2}{n(n^2 – 1)}
\]
\[
r_s = 1 – \frac{6 \times 10}{5(5^2 – 1)} = 1 – \frac{60}{120} = 1 – 0.5 = 0.5
\]
Whakamārama: Ko te uara tauwehenga hononga a Spearman o te 0.5 e tohu ana i te whanaungatanga pai āhua pai i waenga i ngā taurangi X me Y.
Whakamutunga
Mai i ngā tauira i runga ake nei, ka kite tātou me pēhea te whakamahi i te tātari hononga hei whakatau i te kaha me te ahunga o te whanaungatanga i waenga i ngā taurangi e rua. Ka whakamahia te tauwehenga hononga Pearson mō ngā raraunga tau me te whanaungatanga rārangi, ko te tauwehenga hononga Spearman ia ka whakamahia mō ngā raraunga raupapa, raraunga kore-rārangi rānei. Mā te mārama me te matatau ki ēnei tikanga, ka taea e tātou te tātari pai ake i ngā raraunga me te hanga whakatau tika ake i roto i ngā momo mara ako.
